Numerical and experimental investigations of three-dimensional container filling with Newtonian viscous fluids

This work employs numerical and experimental approaches to investigate three-dimensional container filling with Newtonian viscous fluids. For this purpose, a computer code developed for simulating three-dimensional free surface flows has been used. The CFD Freeflow3D code was specifically designed to deal with unsteady three-dimensional flows possessing multiple moving free surfaces. An experimental apparatus that allows the visualization of the various phenomena that can occur during the filling of containers has been constructed and employed. Experiments on container filling were carried out by varying the fluid velocity at the injection nozzle. This paper presents a computational study on container filling with Newtonian viscous fluids and employs the experimental results to validate the software. The experimental observations were compared with the predictions from the Freeflow3D code and good agreement between the two sets of results is observed. Moreover, the code predictions showed that it is capable of capturing the most relevant phenomena observed in the experiments.The Brazilian authors would like to acknowledge the financial support given by the funding agencies: CNPq - Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (Grant Nos. 302631/2010-0, 301408/2009-2, 472514/2011-3), FAPESP - Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (Grant No. 2011/13930-0) and CAPES Grant Nos. BEX 2844/10-9 and 226/09 (CAPES-FCT). This work is part of the activities developed within the CEPID-CeMEAI FAPESP project Grant No. 2013/07375 - 0 and also benefits from the early collaboration within the framework of the University of Sao Paulo (Brazil) and University of Porto (Portugal) research agreements. The Portuguese authors gratefully acknowledge funding from Fundacao para a Ciencia e Tecnologia (FCT) under the project PEst-C/CTM/LA0025/2013 (Strategic Project - LA 25-2013-2014), project PTDC/MAT/121185/2010 and FEDER, via FCT

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids

Structure of full-length wild-type human phenylalanine hydroxylase by small angle X-ray scattering reveals substrate-induced conformational stability

Human phenylalanine hydroxylase (hPAH) hydroxylates l-phenylalanine (l-Phe) to l-tyrosine, a precursor for neurotransmitter biosynthesis. Phenylketonuria (PKU), caused by mutations in PAH that impair PAH function, leads to neurological impairment when untreated. Understanding the hPAH structural and regulatory properties is essential to outline PKU pathophysiological mechanisms. Each hPAH monomer comprises an N-terminal regulatory, a central catalytic and a C-terminal oligomerisation domain. To maintain physiological l-Phe levels, hPAH employs complex regulatory mechanisms. Resting PAH adopts an auto-inhibited conformation where regulatory domains block access to the active site. l-Phe-mediated allosteric activation induces a repositioning of the regulatory domains. Since a structure of activated wild-type hPAH is lacking, we addressed hPAH l-Phe-mediated conformational changes and report the first solution structure of the allosterically activated state. Our solution structures obtained by small-angle X-ray scattering support a tetramer with distorted P222 symmetry, where catalytic and oligomerisation domains form a core from which regulatory domains protrude, positioning themselves close to the active site entrance in the absence of l-Phe. Binding of l-Phe induces a large movement and dimerisation of regulatory domains, exposing the active site. Activated hPAH is more resistant to proteolytic cleavage and thermal denaturation, suggesting that the association of regulatory domains stabilises hPAH.publishe

Finite element simulation of three-dimensional free-surface flow problems

An adaptive finite element algorithm is described for the stable solution of three-dimensional free-surface-flow problems based primarily on the use of node movement. The algorithm also includes a discrete remeshing procedure which enhances its accuracy and robustness. The spatial discretisation allows an isoparametric piecewise-quadratic approximation of the domain geometry for accurate resolution of the curved free surface. The technique is illustrated through an implementation for surface-tension-dominated viscous flows modelled in terms of the Stokes equations with suitable boundary conditions on the deforming free surface. Two three-dimensional test problems are used to demonstrate the performance of the method: a liquid bridge problem and the formation of a fluid droplet

Absence of First-order Transition and Tri-critical Point in the Dynamic Phase Diagram of a Spatially Extended Bistable System in an Oscillating Field

It has been well established that spatially extended, bistable systems that are driven by an oscillating field exhibit a nonequilibrium dynamic phase transition (DPT). The DPT occurs when the field frequency is on the order of the inverse of an intrinsic lifetime associated with the transitions between the two stable states in a static field of the same magnitude as the amplitude of the oscillating field. The DPT is continuous and belongs to the same universality class as the equilibrium phase transition of the Ising model in zero field [G. Korniss et al., Phys. Rev. E 63, 016120 (2001); H. Fujisaka et al., Phys. Rev. E 63, 036109 (2001)]. However, it has previously been claimed that the DPT becomes discontinuous at temperatures below a tricritical point [M. Acharyya, Phys. Rev. E 59, 218 (1999)]. This claim was based on observations in dynamic Monte Carlo simulations of a multipeaked probability density for the dynamic order parameter and negative values of the fourth-order cumulant ratio. Both phenomena can be characteristic of discontinuous phase transitions. Here we use classical nucleation theory for the decay of metastable phases, together with data from large-scale dynamic Monte Carlo simulations of a two-dimensional kinetic Ising ferromagnet, to show that these observations in this case are merely finite-size effects. For sufficiently small systems and low temperatures, the continuous DPT is replaced, not by a discontinuous phase transition, but by a crossover to stochastic resonance. In the infinite-system limit the stochastic-resonance regime vanishes, and the continuous DPT should persist for all nonzero temperatures

A numerical method for simulating viscoelastic flows governed by the integral Maxwell model

The numerical simulation of polymeric flows has attracted the attention of many researchers and a variety of numerical methods for simulating viscoelastic flows has been published in the literature. Most of the techniques solve the constitutive equation in differential form rather than using the integral form. Nonetheless, numerical methods for solving integral models have been developed, most of them using the finite element method on a Lagrangian framework. One difficult in solving integral models is how to compute the Finger strain tensor. In this work we present a numerical method for solving the upper convected Maxwell (UCM) model, given in its integral form, for incompressible viscoelastic flows. We employ the finite difference method and solve the integral equation using an Eulerian mesh. The Finger strain tensor is calculated using the ideas of deformation fields method presented by Peters et. al [1] (see also Hulsen et al. [2]). The equation of motion is solved by the GENSMAC methodology [3] and the integral equation is approximated by a second order quadrature scheme. Convergence results are obtained by considering fully developed flow in a two-dimensional channel and numerical results for the 4:1 planar contraction problem are given

GENSMAC 3D: Implementation of the Navier-Stokes equations and boundary conditions for 3D free surface flows

In the present work we describe a method which allows the incorporation of surface tension into the GENSMAC2D code. This is achieved on two scales. First on the scale of a cell, the surface tension effects are incorporated into the free surface boundary conditions through the computation of the capillary pressure. The required curvature is estimated by fitting a least square circle to the free surface using the tracking particles in the cell and in its close neighbors. On a sub-cell scale, short wavelength perturbations are filtered out using a local 4-point stencil which is mass conservative. An efficient implementation is obtained through a dual representation of the cell data, using both a matrix representation, for ease at identifying neighbouring cells, and also a tree data structure, which permits the representation of specific groups of cells with additional information pertaining to that group. The resulting code is shown to be robust, and to produce accurate results when compared with exact solutions of selected fluid dynamic problems involving surface tension

Numerical solution of the Oldroyd-B model for three-dimensional viscoelastic free surface flows

This work presents a numerical method for solving three-dimensional viscoelastic free surface flows governed by the Oldroyd-B constitutive equation. It is an extension to three dimensions of the technique introduced by Tomé et al. [1] (see also [5]). The governing equations are solved by a finite difference method on a 3D-staggered grid. Marker particles are employed to describe the fluid providing the visualization and the location of the fluid free surface. As currently implemented, the numerical method presented in this work can simulate three-dimensional free surface flows of an Oldroyd-B fluid. The numerical technique presented in this paper is validated by using an exact solution of the flow of an Oldroyd-B fluid inside a pipe. The numerical simulation of the time dependent extrudate swell and jet buckling of viscoelastic fluids are presented

A finite difference technique for simulating unsteady viscoelastic free surface flows

This work is concerned with the development of a numerical method capable of simulating viscoelastic free surface flow of an Oldroyd-B fluid. The basic equations governing the flow of an Oldroyd-B fluid are considered. A novel formulation is developed for the computation of the non-Newtonian extra-stress components on rigid boundaries. The full free surface stress conditions are employed. The resulting governing equations are solved by a finite difference method on a staggered grid, influenced by the ideas of the marker-and-cell (MAC) method. Numerical results demonstrating the capabilities of this new technique are presented for a number of problems involving unsteady free surface flows

Recent advances in the marker and cell method

In this article recent advances in the MAC method will be reviewed. The MAC technique dates back to the early sixties at the Los Alamos Laboratories and this paper starts with a historical review,and then a summary of related techniques. Improvements since the early days of MAC (and the Simplified MAC -SMAC) include automatic time-stepping, the use of the conjugate gradient method to solve the Poisson equation for the corrected velocity potential, greater efficiency through stripping out all particles (markers) other than those near the free surface , more accurate approximations of the free surface boundary conditions, the addition of a bounded high accuracy upwinding for the convected terms (thereby being able to solve higher Reynolds number flows), and a (dynamic) flow visualization facility. This article will concentrate, in the main, on a three-dimensional version of the SMAC method. It will show how to approximate curved boundaries by onsidering one configurational example in detail; the same will also be done for the free surface. The article will avoid validation, but rather focus on many of the examples and applucations that the MAC method can solve from turbulent flows to rheology. It will conclude with some speculative comments on the future direction of the methodology